Parametric generalization of Baskakov operators

Abstract

Herein we propose a non-negative real parametric generalization of Baskakov operators and call them alpha-Baskakov operators. We show that alpha-Baskakov operators can be expressed in terms of divided differences. Then, we obtain the nth order derivative of alpha-Baskakov operators in order to obtain its new representation as powers of independent variable x. In addition, we obtain Korovkins-type approximation properties of alpha-Baskakov operators. Moreover, by using the modulus of continuity, we obtain the rate of convergence. Numerical results presented show that depending on the value of the parameter alpha, an approximation to a function improves compared to classical Baskakov operators.